Predicting prey population dynamics from kill rate, predation rate and predator-prey ratios in three wolf-ungulate systems

1. Predation rate (PR) and kill rate are both fundamental statistics for understanding predation. However, relatively little is known about how these statistics relate to one another and how they relate to prey population dynamics. We assess these relationships across three systems where wolf-prey dynamics have been observed for 41 years (Isle Royale), 19 years (Banff) and 12 years (Yellowstone). 2. To provide context for this empirical assessment, we developed theoretical predictions of the relationship between kill rate and PR under a broad range of predator-prey models including predator-dependent, ratio-dependent and Lotka-Volterra dynamics. 3. The theoretical predictions indicate that kill rate can be related to PR in a variety of diverse ways (e. g. positive, negative, unrelated) that depend on the nature of predator-prey dynamics (e. g. structure of the functional response). These simulations also suggested that the ratio of predator-to-prey is a good predictor of prey growth rate. That result motivated us to assess the empirical relationship between the ratio and prey growth rate for each of the three study sites. 4. The empirical relationships indicate that PR is not well predicted by kill rate, but is better predicted by the ratio of predator-to-prey. Kill rate is also a poor predictor of prey growth rate. However, PR and ratio of predator-to-prey each explained significant portions of variation in prey growth rate for two of the three study sites. 5. Our analyses offer two general insights. First, Isle Royale, Banff and Yellowstone are similar insomuch as they all include wolves preying on large ungulates. However, they also differ in species diversity of predator and prey communities, exploitation by humans and the role of dispersal. Even with the benefit of our analysis, it remains difficult to judge whether to be more impressed by the similarities or differences. This difficulty nicely illustrates a fundamental property of ecological communities. Second, kill rate is the primary statistic for many traditional models of predation. However, our work suggests that kill rate and PR are similarly important for understanding why predation is such a complex process.